Chapter 6.8, Problem 420E

For the following exercises, use a CAS and the divergence theorem to compute the net outward flux for the vector fields across the boundary of the given regions D.

420. [T] Use a CAS to calculate the flux of $F\left(x,y,z\right)=\left(x^3+y\sin z\right)i+\left(y^3+z\sin x\right)j+3zk$ across surface S, where S is the boundary of the solid bounded by hemispheres $z=\sqrt{4-x^2-y^2}$ and $z=\sqrt{1-x^2-y^2}$ , and plane $z=0$ .